摘要
考察了非线性Dirichlet边值问题w″(x) -λw(x) +f(x ,w(x) ) =0 ,0≤x≤ 1 ;w( 0 ) =w( 1 ) =0的解和正解的存在性与多解性 ,其中λ>-π2 并且f∶[0 ,1 ]× ( -∞ ,+∞ )→ ( -∞ ,+∞ )
The existence and multiplicity of solutions and positive solutions are considered for the nonlinear Dirichlet problem w″(x)-λw(x)+f(x,w(x))=0, 0≤x≤1; w(0)=w(1)=0, where λ>-π 2 and f\%∶\%[0,1]×(-∞ ,+∞ )→(-∞,+∞ ) is bounded-below.
关键词
二阶Dirichlet问题
解和正解
存在性
多解性
second-order Dirichlet problem
solution and positive solution
existence
multiplicity
